No idea, but I wouldn't expect Intel to offer less options on Linux? Unless it's unsupported in general.

It can depend, some TVs are very good at upscaling. It's just my general experience that LCD monitors are usually worse at it. Plus there's integer scaling now, which removes pretty much all scaling issues through software IMO.

pah, blatantly ignores the best choice with options for native 4:3 scaling set from the monitor,integrated speakers small size 20" for the small desk and the raspberry not to mention the price of 77 dollars

but i do agree with the others, go with crt, it will probably be a life saver

I have my Raspberry Pi 4 connected to my 65" TV in the living room as I am using the RPi4 also as my always-online media center, watching movies, videos etc. with it. I control it with a wireless keyboard and mouse from the sofa.

I can also connect to the RPi4 from my other PCs remotely, by using remote desktop software like TeamViewer, AnyDesk or Google Chrome Remote (at least the first two have Raspberry Pi support too, and I presume Chrome Remote too as it is supposed to work on any Chrome (and Chromium?) browser-equipped computer).

EDIT: Oh, ok, so the new monitor is supposed to be used with another (desktop) PC, not the RPi4? Whatever.

EDIT2: I am actually unsure how common "computer monitors with built-in speakers" are. I guess they are there, I just practically never see modern computer monitors with speakers, and usually the "monitors" with speakers are actually small-size TVs with remote control, TV tuner and all. You can get those quite cheap too.

One other thing: I don't really have the room for a CRT, and I would like something modern, anyway.

how about something from the samsung line up such as the samsung S24F352 not sure about the 4:3 settings from the screen menu, my personal desktop is a S27C570, no speakers but with a monitor setting to switch between 16:9 and 4:3, 4:3 will display 640x480 proper, and it is probably mentioned before but if you find the intel control menu for the integrated graphics chip from there you can choose between different aspect ratio's

the S24F352 is around 100 euro's so you might find a cheaper version in the us not to mention with money left to buy some cheap standalone 2.0 speaker set wich you can either attach to the wall, with some gum or place behind or maybe even next to the monitor

"So, any thoughts? (I have had Sceptre recommended to me; is that any good?)"
yes use google or similar

In ye olden days, you'd handwrite the right "modeline" in xorg.conf or XF86Config.
AFAIK, you still can.
I think you can achieve the same with "xrandr". I had an Intel chip I used xrandr to get an unusual two monitor setup going on.
It's been years since I had to do kinky stuff like that, so the memory is a bit fuzzy.

Using xrandr to set a 640x480 or other non-widescreen resolution on my current display results in a stretched image, and I need to press a button on the remote in order to fix it; this happens every time I try to do this.

It is this stretched image and having to press the button on the remote that I would like to avoid.

Fair enough, but have your checked the advanced arguments that xrandr can take?

I just checked the manpage, and a search for "ratio" yields no hits, except for instances of the word "configuration".

You can specify new modes with custom modelines. That allows a lot of tweaking, but is a bit of an arkane art.
I wonder if setting the horizontal underscan might be enough.

Someone recommended the ViewSonic VA2456-MHD to me. Is that a decent monitor? Does it handle non-widescreen video signals (like 640x480) in a sensible manner?

One other thought: One other problem with having the computer re-scale the image is that it's not unusual for computers to output a 640x480 signal during the early parts of the boot process, before the OS has loaded. (For example, in the BIOS or on the GRUB/Syslinux boot menu.)

Dell, They have the option for 4.3

I have seen some Asus monitors have the options for 4.3 res.